The Outlook of the Sovereign Planner: The Linear Activity Model
The purpose of this chapter is to formulate a linear numerical general equilibrium model. The model is essentially a Leontief type of input–output model, extended with resource constraints. In this chapter the equilibrium model is developed and analysed u
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The Outlook of the Sovereign Planner: The Linear Activity Model
The purpose of this chapter is to formulate a linear numerical general equilibrium model. The model is essentially a Leontief type of input–output model, extended with resource constraints. In this chapter the equilibrium model is developed and analysed under conditions of competitive market behaviour. To provide the reader with an understanding of the nature of this model and its link to economic theory, the concept of welfare optimum (Pareto efficiency) and its logical relation to competitive equilibrium is used as a connecting thread between the concept of economic equilibrium and the mathematical programming formulation. The following sections will highlight the major features of the model. At the same time, the assumptions necessary to make the model operational are made explicit.
2.1
Commodities and Activities
In this study we shall be considering an economy where there exists a finite number of commodities (commodity groups)1 subject to production, consumption, or both. The commodity concept also includes services. A commodity is characterised by the property that two equal quantities of it are completely equivalent for each consumer and each producer. The commodities are here divided into two groups, according to whether they are produced within the production system or not. Commodities in the former group are called produced commodities, in the latter group, primary commodities.2 Thus, total supply within the economic system specified in this study is a result of the domestic production system. 1 Generally, a commodity is defined by its physical characteristics, its location, and the date of its delivery. Commodities differing in any of these characteristics will be regarded as different. However, in this model a commodity is synonymous with the industry supplying the commodity (sector classification principle). 2 Thus, there is only use of primary commodities, not production of them.
R. Nore´n, Equilibrium Models in an Applied Framework, Lecture Notes in Economics and Mathematical Systems 667, DOI 10.1007/978-3-642-34994-2_2, # Springer-Verlag Berlin Heidelberg 2013
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2.2
2 The Outlook of the Sovereign Planner: The Linear Activity Model
Producers
The n producers (industries) execute the production programs represented by the n nonnegative multiples Zj of aij. The extent to which the activity is utilised must be feasible, i.e. to say the produced amount Zj must be an element of the production set Yj. For any producer j there exists a given quantity of capital commodities, previously produced commodities, and in the short run specific for each produced commodity, and hence, each producer. In other words, capacities are assumed immobile. For the producer each activity implies a given transformation of primary commodities into produced commodities, and to make this transformation possible, a given quantity of capacities available. By this specification, the capacities are considered as primary commodities. Hence, the primary commod
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